On the use of rotational splitting asymmetries to probe the internal rotation profile of stars. Application to β\beta Cephei stars

Rotationally-split modes can provide valuable information about the internal rotation profile of stars. This has been used for years to infer the internal rotation behavior of the Sun. The present work discusses the potential additional information that rotationally splitting asymmetries may provide when studying the internal rotation profile of stars. We present here some preliminary results of a method, currently under development, which intends: 1) to understand the variation of the rotational splitting asymmetries in terms of physical processes acting on the angular momentum distribution in the stellar interior, and 2) how this information can be used to better constrain the internal rotation profile of the stars. The accomplishment of these two objectives should allow us to better use asteroseismology as a test-bench of the different theories describing the angular momentum distribution and evolution in the stellar interiors.Comment: 4 pages, 2 figures; IV International Helas conference proceedings (refereed). To be published in Astronomical Note

FILOU oscillation code

The present paper provides a description of the oscillation code FILOU, its main features, type of applications it can be used for, and some representative solutions. The code is actively involved in CoRoT/ESTA exercises (this volume) for the preparation for the proper interpretation of space data from the CoRoT mission. Although CoRoT/ESTA exercises have been limited to the oscillations computations for non-rotating models, the main characteristic of FILOU is, however, the computation of radial and non-radial oscillation frequencies in presence of rotation. In particular, FILOU calculates (in a perturbative approach) adiabatic oscillation frequencies corrected for the effects of rotation (up to the second order in the rotation rate) including near degeneracy effects. Furthermore, FILOU works with either a uniform rotation or a radial differential rotation profile (shellular rotation), feature which makes the code singular in the field.Comment: 6 pages, 5 figures. Astrophysics and Space Science (in press

The eigenvalues of limits of radial Toeplitz operators

Let $A^2$ be the Bergman space on the unit disk. A bounded operator $S$ on $A^2$ is called radial if $Sz^n = \lambda_n z^n$ for all $n\ge 0$, where $\lambda_n$ is a bounded sequence of complex numbers. We characterize the eigenvalues of radial operators that can be approximated by Toeplitz operators with bounded symbols.Comment: 14 page

The role of rotation on Petersen Diagrams. II The influence of near-degeneracy

In the present work, the effect of near-degeneracy on rotational Petersen diagrams (RPD) is analysed. Seismic models are computed considering rotation effects on both equilibrium models and adiabatic oscillation frequencies (including second-order near-degeneracy effects). Contamination of coupled modes and coupling strength on the first radial modes are studied in detail. Analysis of relative intrinsic amplitudes of near-degenerate modes reveals that the identity of the fundamental radial mode and its coupled quadrupole pair are almost unaltered once near-degeneracy effects are considered. However, for the first overtone, a mixed radial/quadrupole identity is always predicted. The effect of near-degeneracy on the oscillation frequencies becomes critical for rotational velocities larger than 15-20 km/s, for which large wriggles in the evolution of the period ratios are obtained (up $10^{-2}$). Such wriggles imply uncertainties, in terms of metallicity determinations using RPD, reaching up to 0.50 dex, which can be critical for Pop. I HADS (High Amplitude \dss). In terms of mass determinations, uncertainties reaching up to 0.5 M_sun are predicted. The location of such wriggles is found to be independent of metallicity and rotational velocity, and governed mainly by the avoided-crossing phenomenon.Comment: 8 pages, 7 figures, 1 table. (accepted for publication in A&A

Surface-induced magnetism in C-doped SnO2_{2}

The magnetism of C-doped SnO$_{2}$ (001) surfaces is studied using first-principles calculations. It is found that carbon does not induce magnetism in bulk SnO$_{2}$ when located at the oxygen site, but shows a large magnetic moment at the SnO$_{2}$ (001) surface. The magnetic moment is mainly contributed by the carbon atoms due to empty minority spins of $p$ orbitals and is localized at the surface and subsurface atoms. No magnetism is observed when the carbon atom is located at the subsurface oxygen sites. The origin of magnetism is discussed in the context of surface bonding.Comment: 3 pages, 3 figure

Cyclic extensions are radical

We show that finite Galois extensions with cyclic Galois group are radical.Comment: 1 page. This has been published as filler in the American Mathematical Monthl